A solid sphere of radius 3 cm is melted to form a right circular cone such that the height of the cone is half the radius of the cone. Find the radius of the cone.

Question

Question

Answer 1

GIVEN:

Radius of sphere = 3 cm

Height of the cone = Half of the radius of the cone

CONCEPT:

Volume of Sphere = Volume of Cone

FORMULA USED:

Volume of Sphere = 4/3 × πR³

Volume of Cone = 1/3 × πr²h

CALCULATION:

Suppose the height and radius of the cone are ‘h’ and ‘r’ respectively.

∴ h = r/2

Now,

Applying the formula:

\(\frac{4}{3} \times \pi \times 3 \times 3 \times 3 = \frac{1}{3} \times \pi \times r \times r \times h\)

Put h = r/2

⇒ \(\frac{4}{3} \times 3 \times 3 \times 3 = \frac{1}{3} \times r \times r \times \frac{r}{2}\)

⇒ r³ = 216

⇒ r = 6

∴ Radius of the cone = 6 cm.

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